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Dam-break flows: acquisition of experimental data through an imaging technique and 2D numerical modelling
No full textThis paper presents experimental and two-dimensional 2D numerical results of four tests concerning rapidly varying flows
induced by the sudden removal of a sluice gate. For the acquisition of the experimental data, an imaging technique capable of providing
spatially distributed information was adopted: a coloring agent was added to the water, the opalescent bottom of the facility was
backlighted, and photographs of the area of interest were taken. The gray tones of the acquired images were converted into water depths
by means of transfer functions derived from a static calibration. The potential sources of error of the proposed procedure are discussed.
A local comparison with an ultrasonic device showed a 20% maximum deviation in 95% of the observations. The tests were simulated
through a 2D MUSCL-Hancock finite volume numerical model, based on the classical shallow water approximations, in which the
intercell water depths are estimated according to the surface gradient method. A global analysis of the relative frequency distributions of
the deviation between numerical and experimental results is performed. Despite some evident differences at a local scale, the adopted 2D
numerical model is capable of reproducing the main features of the flow fields under investigation
Closure to " Dam-break flows: acquisition of experimental data through an imaging technique and 2D numerical modelling"
No full textThe writers thank the discussers for their interest in the paper,
their valuable remarks, and the opportunity to further discuss the
imaging experimental technique and the numerical results presented in the original paper. The described laboratory work aimed to widen the experimental database useful for validating dambreak numerical models, and the writers are pleased that the discussers found the provided data helpful to assess the capability of a widespread commercial software of handling this kind of process
A weighted surface-depth gradient method for the solution of the 2D shallow water equations
No full textThe two dimensional shallow water equations (SWE) are currently accepted as a mathematical basis for the study of several rapidly varying flows, such as those induced by dam breaking or embankment failure. Among the many methodologies available for the numerical integration of SWE, the finite volume MUSCL-Hancock cell-centred schemes are nowadays frequently used. These schemes should also include a robust and efficient treatment of the bottom source term in order to track the wetting and drying fronts and to preserve the static condition of a quiescent fluid over an irregular topography (C–property).
In particular the Surface Gradient Method (SGM – Zhou et al. 2001) computes water depth at the intercells from the extrapolation of the water surface level and introduces the bottom slope source term through a centred unsplit discretization; it can satisfy the C-property on a Cartesian grid even on irregular topographies, but it is not efficient in tracking wetting and
drying fronts. On the other hand, many schemes that evaluate water depth at the cell interfaces through the extrapolation of the same conserved variable (Depth Gradient Method, DGM) and
perform the splitting of the bed slope source term, do not satisfy the C-property, but are robust and stable near moving boundaries. In this paper a Weighted Surface-Depth Gradient Method, capable of preserving the good capabilities of the previously mentioned methods, is proposed. In the framework of the SGM scheme, the water depth at cell interfaces is estimated through a weighted average of the boundary extrapolated values deriving from MUSCL DGM and SGM reconstructions. The weight parameter is evaluated on the basis of the local Froude number through a formulation that allows a smooth transition between a fully SGM and a fully DGM treatment. The numerical scheme is validated through the application to some reference test cases whose exact solution is available in literature. The first set of tests concerns 1D steady flows on a steep parabolic bump in a rectangular frictionless channel (Liska & Wendroff 1998); the
second deals with two exact solutions (Thacker 1981) related to the periodic motion of a volume of water in a frictionless basin whose shape is a parabola of revolution. In all the tests the results obtained by the application of the Weighted Surface-Depth Gradient Method are better or, at least, equal to those obtained by the SGM or DGM schemes
A Weighted Surface-Gradient Method for the integration of 2D shallow water equations with topography
No full textA finite volume MUSCL scheme for the numerical integration of 2D shallow water equations is presented.
In the framework of the SLIC scheme, the proposed weighted surface-depth gradient method (WSDGM) computes intercell water depths through a weighted average of DGM and SGM reconstructions, in which the weight function depends on the local Froude number. This combination makes the scheme capable of performing a robust tracking of wet/dry fronts and, together with an unsplit centered discretization of the bed slope source term, of maintaining the static condition on non-flat topographies (C-property). A correction
of the numerical fluxes in the computational cells with water depth smaller than a fixed tolerance enables a drastic reduction of the mass error in the presence of wetting and drying fronts. The effectiveness
and robustness of the proposed scheme are assessed by comparing numerical results with analytical and reference solutions of a set of test cases. Moreover, to show the capability of the numerical model on
field-scale applications, the results of a dam-break scenario are presented
An Imaging Technique for Laboratory Water Depth Measurement of Rapidly Varying Flows
No full textA recently proposed technique based on high resolution digital images for the acquisition of water depths in rapidly varying free surface flows is discussed. The addition of a coloring agent to the water allows to obtain a spatially distributed information of depths after the image conversion through a proper transformation function derived from a preliminary calibration. This technique was validated on the
basis of the results of some laboratory dam-break tests by comparing water depth time series obtained from the post-processing of images with those returned by ultrasonic distance meters in six gauge locations. The influence of RAW and JPEG acquisition formats was investigated. The results show an accuracy comparable to
that of ultrasonic transducers. The proposed imaging technique is thus preferable thanks to its capability of acquiring distributed water depth information for flows characterized by high spatial variability
Flood hazard mapping by means of fully-2D and quasi-2D numerical modeling: a case study
No full textThe results of mathematical modeling of some flooding scenarios in the middle reach of the
more important Italian river are presented. In 1868 and 1951 the considered region was subject to two severe
floods, due to the breaking of the earthen embankment of the Po river. The inundated area was about 40km2 and
water depths up to 3.5 meters were observed. In both cases the breaches were originated by the failure of sluice
gates located on minor drainage channels. On the basis of the shallow water approach, four flooding scenarios
were at first simulated by means of a 2D finite volume MUSCL-Hancock code. The scheme is explicit, shock
capturing, high resolution and belongs to the Surface Gradient Methods class. The SGM peculiar way of treatment
of the slope source term allows to rigorously satisfy the C-property and to model the potential overtopping
of the man-made or natural levees, such as channel embankments, roads, railways, etc. To derive the discharge
overflowing from the breach, also when the flow is backwatered due to the partial filling of the floodable region,
a reach of the Po river was included in the calculations. A sensitivity analysis on the main parameters affecting
the inundation dynamics, namely the breach width and its position and time of occurrence with reference to the
chosen hydrological input, was performed. At the aim to derive a flood hazard mapping for the area under investigation
a risk factor was also derived as a function of computed maximum water depth and arrival time of the
wetting front. One of the investigated scenarios, assumed as a reference, was also simulated by means of a
quasi-2D numerical model. The area susceptible to flooding was schematized through a number of storage cells,
each representing a portion of the domain bounded by the same levees considered in the two dimensional
model. The cells were properly joined by link channels provided with features that allow to compute the flow
over user defined broad crested weirs. The flooding dynamics is not correctly described by the quasi-2D numerical
model in the first hours after the breaching; afterwards the quasi-static behaviour of the flooding is well
caught. However the overall comparison between the fully-2D and quasi-2D numerical results shows a fairly
good agreement for what concerns the identification of flooded area, maximum water depths and discharge
overflowing from the breach
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